resonance circuit

[blackseaman]

hi, would u pls show me with a programme or just by saying how a current will be there if we energize a circuit in which the capacitive reactance and inductive reactance is equeal to each other and there is also a resistance.
it is easy to see that in steady state the current will be sinusoidal but i cant see how it will be in transient state...

 

[blackseaman]

maybe with pspice or ecad ,or just saying how will the current behave at the energisation moment...

 

[electricpete]

I'm picturing series RLC circuit with suddenly applied ac voltage. I imagine it is also a simple enough circuit to be solved using Laplace transform or other differential equation techniques. The answer depends in part on the angle of the voltage source at moment of switch closing.

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[magoo2]

In the transient state, the L and C combo set up a natural frequency. This sets up usually a higher frequency ringing. As pete points out, you have some R. This provides damping.

Think of the voltage across the capacitor. Initially is is zero because it is not switched on or energized. Once you energize, the capacitor voltage can't change instantaneously, so starts off at a zero voltage and tracks the fundamental frequency voltage with the addition of the damped natural frequency component. There's overshoot involved too so it's not simply fundamental plus natural frequency.

You can find a lot of examples with waveforms if you search on capacitor switching or capacitor energizing.

 

[electricpete]

You specified XL = XC, that means a resonant condition

If it is a series R/L/C circuit, than at resonance the series combination of XL and XC produces a zero impedance, the steady state source current is determined by the resistance.

If it is a parallel R/L/C circuit, than at resonance the parallel combination of XL and XC produces an infinite impedance the steady state current provided by the source is determined by the resistance. There will very high (theoretically infinite) current circulating in the loop containing L and C, but it does not affect the source current or the resistor current because it flows in a loop through only L and C... impedance seen from outside that loop is infinite.

Which are you interested in?

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[electricpete]

Attached is a plot of series R/L/C resonant circuit with suddenly applied voltage source. The parameters selected for this simulation are on tab "main".

If you follow the instructions, you can vary the parameters and rerun the simulation. Different behavior will result from different R. As magoo said, lower R means less damping, longer to get reach the steady state amplitude. Also the relative values of L and C (we can increase one and decrease the other and keep the same resonant frequency) have some affect as well as angle of closing.

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